Calculus Answers

Find the absolute maximum and absolute minimum values of f(x)=(x^2−4)/(x^2+4) on the interval [−5,5].

List the critical numbers of the following function in increasing order. Enter N in any blank that you don't need to use.

f(x)=3x^3+3x^2−3x

...............
..............
..............

Find the absolute and local maximum and minimum values of f(x)={x^2 −1≤x<0
{2−x^2 0≤x≤1.
If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.

Absolute maxima
x = y =
x = y =
x = y =

Absolute minima
x = y =
x = y =
x = y =

Local maxima
x = y =
x = y =
x = y =

Local minima
x = y =
x = y =
x = y =

Find the absolute maximum and absolute minimum values of f(x)=x^3−6x^2+9x+6 on the interval [−1,4].

Find the absolute maximum and absolute minimum values of f(x)=x−lnx on the interval [1/8,8].

find the second derivative of x^1/2

A high-speed bullet train accelerates and decelerates at the rate of 10 ft/s2. Its maximum cruising speed is 75 mi/h. (Round your answers to three decimal places.)
(a) What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes?
. mi

(b) Suppose that the train starts from rest and must come to a complete stop in 15 minutes. What is the maximum distance it can travel under these conditions?
mi

(c) Find the minimum time that the train takes to travel between two consecutive stations that are 37.5 miles apart.
min

(d) The trip from one station to the next takes at minimum 37.5 minutes. How far apart are the stations?

QUESTION 4
A controller spots two planes at the same altitude flying toward each other (see figure). Their
flight paths are
0
20 SW
and
0
45 SE
. One plane is 150 miles from point P with a speed of
375 miles per hour. The other is 190 miles from point P with a speed of 450 miles per hour.

a) Find parametric equations for the path of each plane where
t
is the time in hours, with
0t 
corresponding to the time at which the air traffic controller spots the planes.
b) Use the result in part (a) to write the distance between the planes as a function of
t
.
c) Use a graphing utility to graph the function in part (b). When will the distance
between the planes be minimum? If the planes must keep a separation of at least 3
miles, is the requirement met?

if a 14-i\units vector makes an angle of 45 degree with the horizontal, wht r its horizontal and vertical components